Evaluate: g. `5 (1)/(3) xx 8 (1)/(4) xx 2 (3)/(5)`

Answer

To evaluate the expression \( 5 \frac{1}{3} \times 8 \frac{1}{4} \times 2 \frac{3}{5} \), we will follow these steps:

### Step 1: Convert Mixed Numbers to Improper Fractions
1. Convert \( 5 \frac{1}{3} \) to an improper fraction:
\[ 5 \frac{1}{3} = \frac{5 \times 3 + 1}{3} = \frac{15 + 1}{3} = \frac{16}{3} \]

2. Convert \( 8 \frac{1}{4} \) to an improper fraction:
\[ 8 \frac{1}{4} = \frac{8 \times 4 + 1}{4} = \frac{32 + 1}{4} = \frac{33}{4} \]

3. Convert \( 2 \frac{3}{5} \) to an improper fraction:
\[ 2 \frac{3}{5} = \frac{2 \times 5 + 3}{5} = \frac{10 + 3}{5} = \frac{13}{5} \]

### Step 2: Multiply the Improper Fractions
Now we multiply the improper fractions:
\[ \frac{16}{3} \times \frac{33}{4} \times \frac{13}{5} \]

### Step 3: Multiply the Numerators and Denominators
1. Multiply the numerators:
\[ 16 \times 33 \times 13 \]

2. Multiply the denominators:
\[ 3 \times 4 \times 5 \]

### Step 4: Calculate the Denominator
Calculating the denominator:
\[ 3 \times 4 = 12 \]
\[ 12 \times 5 = 60 \]

### Step 5: Calculate the Numerator
Calculating the numerator:
1. First, calculate \( 16 \times 33 \):
\[ 16 \times 33 = 528 \]
2. Then multiply by 13:
\[ 528 \times 13 \]
- \( 528 \times 10 = 5280 \)
- \( 528 \times 3 = 1584 \)
- Adding these together:
\[ 5280 + 1584 = 6864 \]

### Step 6: Form the Final Fraction
Now we have:
\[ \frac{6864}{60} \]

### Step 7: Simplify the Fraction
To simplify \( \frac{6864}{60} \), we can divide both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 6864 and 60 is 12.
\[ \frac{6864 \div 12}{60 \div 12} = \frac{572}{5} \]

### Final Answer
Thus, the final answer is:
\[ \frac{572}{5} \]

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